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Pages:
3 pages/≈825 words
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Style:
APA
Subject:
Mathematics & Economics
Type:
Math Problem
Language:
English (U.S.)
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Date:
Total cost:
$ 14.58
Topic:

Covariance and Correlation

Math Problem Instructions:

Please help me finish the 3 questions, let me know if you have any questions or concerns.

Problem 1:

Please calculate the covariance and correlation between the following two variables. Please show your work (you can take a picture if done by hand).

Correlation:

Problem 2:

According to the U.S. Department of Education, full-time graduate students receive an average salary of $12,800 with a standard deviation of $1800. The dean of graduate studies at a large state university in PA claims that his graduate students earn more than this. He surveys 46 randomly selected students and finds their average salary is $13,445. With alpha = 0.05, is the dean’s claim correct?

Read the question carefully to see what information is available to decide which test will be applicable. Be sure to include all the relevant steps of hypothesis testing (null and alternative hypotheses, test statistic, critical value, decision rule and the final decision with interpretation). I am going to let you decide if you want to do a one-tail or two-tail test (I will accept either).

Problem 3:

You have been provided with a data set ‘Wall.xlsx’  to analyze information on selected aspects of state educational performance outcomes, resource inputs, and population characteristics, in 2017. You will be preparing a short brief (up to one page in text) for a team of education officers at the US Department of Education to discuss where to invest more resources to improve average high-school graduation rates statewide.  

The brief will include some descriptive statistics (such as mean, median, standard deviation, skewness, kurtosis) to describe each of the four variables provided. Further, please include plots (histograms, scatterplots) and correlations to show the relationship between the dependent variable, average high-school graduation rate statewide (HSGRADRT), and independent variables that include average teacher salary statewide (TCHRSAL), average number of students per teacher statewide (STRATIO) and average expenditure per pupil statewide (PPEXPEND). 

Based on correlation tests, you will choose one independent variable, that you think might affect the high-school graduation rates the most and to do a bivariate regression. 

Please make sure to interpret these statistics. For example, which independent variable has the largest correlation with high-school graduation rates. What does it mean to have the largest correlation, etc. Do not just say correlations are strong or negative. Explain what that means.

Math Problem Sample Content Preview:
Homework Assignment 2
Problem 1:
Please calculate the covariance and correlation between the following two variables. Please show your work (you can take a picture if done by hand).
Variable 1

Variable 2

1

13

3

12

6

15

6

14

8

13

Mean = 4.8

Mean = 13.4

Standard Deviation = 2.77

Standard Deviation = 1.14

Covariance:
Covariance: cov(x, y) = Σ(xᵢ - μx)(yᵢ - μy) / (n - 1)
where
x = Variable 1
y = Variable 2
μx = mean of x
μy = mean of y
n = number of data points
xᵢ - μx

yᵢ - μy

(xᵢ - μx)(yᵢ - μy)

-3.8

-0.4

7.52

-1.8

-1.4

3.96

1.2

1.6

1.92

1.2

0.6

0.72

3.2

-0.4

-1.28

Total

13.84

Using the formula for covariance, we can calculate:
cov(x, y) = Σ(xᵢ - μx)(yᵢ - μy) / (n - 1)
= 13.84 / 4
= 3.46
Correlation:
Correlation, corr(x, y) = cov(x, y) / (σx * σy)
where:
x = Variable 1
y = Variable 2
σx = standard deviation of x
σy = standard deviation of y
n = number of data points
corr(x, y) = cov(x, y) / (σx * σy)
= 3.46 / (2.77 * 1.14)
= 1.04
Problem 2:
According to the U.S. Department of Education, full-time graduate students receive an average salary of $12,800 with a standard deviation of $1800. The dean of graduate studies at a large state university in PA claims that his graduate students earn more than this. He surveys 46 randomly selected students and finds their average salary is $13,445. With alpha = 0.05, is the dean’s claim correct?
Read the question carefully to see what information is available to decide which test will be applicable. Be sure to include all the relevant steps of hypothesis testing (null and alternative hypotheses, test statistic, critical value, decision rule and the final decision with interpretation). I am going to let you decide if you want to do a one-tail or two-tail test (I will accept either).
A one-tailed hypothesis test is ideal for the case because the dean is claiming that his graduate students earn more than the national average.
Null Hypothesis: The average salary of graduate students at the state university is not significantly different from the national average salary ($12,800).
Alternative Hypothesis: The average salary of graduate students at the state university is significantly higher than the national average salary ($12,800).
Given that the standard deviation is unknown, the t-test will b...
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